Probability Density Evolution Method for Seismic Reliability Evaluation of Structural Systems

A structural system reliability evaluation approach based on the idea of equivalent extreme-value event and the probability density evolution method is presented. Using the idea of equivalent extreme-value event, for a compound random event as combination of a set of random events, an equivalent extreme-value event could be constructed. So, this makes it possible to transform computation of the probability of the compound random event to a one-dimensional integration of the probability density function of the equivalent extreme-value random variable. In conjunction with the probability density evolution method, which is capable of evaluating the extreme-value distribution of a set of random variables or stochastic processes, the structural system reliability could be evaluated through computing the probability of the equivalent extreme-value event. The proposed approach is discussed in detail on how to construct the equivalent extreme-value event and then implement the procedure numerically. On the other hand, based on the orthogonal expansion method, the stochastic process of earthquake ground motion can be represented as a linear combination of deterministic functions modulated by a set of mutually independent random variables. Combining the above methods, the reliability of structures under earthquake excitations could be successfully evaluated. An example, of which deals with a linear frame structure subjected to non-stationary seismic loading, is illustrated to validate the proposed method.